Sources and propagation of errors in quantitative phase imaging techniques using optical interferometry

Quantitative phase imaging (QPI) has many applications in a broad range of disciplines from astronomy to microbiology. QPI is often performed by optical interferometry, where two coherent beams of light are used to produce interference patterns at a detector plane. Many algorithms exist to calculate the phase of the incident light from these recorded interference patterns as well as enhance their quality by various de-noising methods. Many of these de-noising algorithms, however, corrupt the quantitative aspect of the measurement, resulting in phase contrast images. Among these phase calculation techniques and de-noising algorithms, none approach the optimization of phase measurements by theoretically addressing the various sources of error in its measurement, as well as how these errors propagate to the phase calculations. In this work, we investigate the various sources of error in the measurements required for QPI, as well as theoretically derive the influence of each source of error on the overall phase calculation for three common phase calculation techniques: the four bucket/step method, three bucket/step method, and the Carré method. The noise characteristics of each of these techniques are discussed and compared using error parameters of a readily available CCD sensor array. Additionally, experimental analysis is conducted on interferograms to investigate the influence of speckle noise on the phase measurements of the three algorithms discussed